Answer:
B. [tex]y=\frac{1}{2}x+7[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given a scatter plot and we are asked to find the equation that could represent the relationship shown in the scatter plot.
Let us see our given choices one by one.
A. [tex]y=-x+8[/tex]
The given equation has a negative slope, which indicates that when x variable will increase y variable will decrease.
We can see that our data trend has a positive correlation as x variables are increasing our y variables are also increasing, therefore, option A is not a correct choice.
B. [tex]y=\frac{1}{2}x+7[/tex]
We can see from our given data that with each increase in x variables approximately all y variables increase by half.
If we draw a line of best fit, it will pass through point (0,7), which will be y-intercept of our line. We can see from our attachment that approximately all the points are equidistant from our line of best fit.
Therefore, option B is the correct choice.
C. [tex]y=3x[/tex]
This equation represents a slope of 3, which means with each increase in x our y variables will increase 3 times as x. As y-intercept is not given, this means that y-intercept will be at origin (0,0). If we draw a line passing origin with a slope of 3, almost data points will lie below that line.
As y variables are not increasing three times as x variables, therefore, option C is not a correct choice either.
D. [tex]y=\frac{5}{2}x-1[/tex]
If we draw a line passing through point (0,-1) with a slope of 2.5, almost data points will lie above that line. Therefore, option D is not a correct choice as well.
